Duality
in Field Theories| Duality
in Field Theories |
In Electromagnetic Theory > s.a. [electromagnetism]; integrable
systems.
* Idea: The transformations
of the quantities {(
e,
m),
(je, jm),
(E, H), (D, B)}, defined
by
xe = xe' cos 
+ xm' sin , xm = –xe' sin + xm' cos .
* Properties: The values
of E × H, E · D + B · H, Tab,
and the Maxwell equations, are left invariant.
* Applications: Duality
between the Aharonov-Bohm and Aharonov-Casher effects.
@ General references: Misner & Wheeler AP(57);
Montonen & Olive PLB(77)
[monopole]; Zhu
JPA(89)
[complexions]; Anandan gq/95 [topological
phases]; Witten SelMath(95)ht [on
a general manifold]; Deser & Sarioglu PLB(98)ht/97 [and
Lorentz invariance]; Igarashi et al NPB(98)ht;
Hatsuda et al NPB(99)ht [invariant
lagrangians]; Li & Naón
MPLA(01)ht/00;
Przeszowski JPA(05)ht [light-front
variables]; Julia ht/05-in
[generalization]; Barnich & Troessaert JMP(09)-a0812 [as
bi-Hamiltonian system]; Bakas a0910 [rev, and gravity].
@ In quantum electrodynamics: Buhmann & Scheel PRL(09)-a0806 [macroscopic].
@ In non-linear electrodynamics: Gibbons & Rasheed NPB(95)ht; Gaillard & Zumino ht/97,
ht/97 [non-linear].
@ From Lagrangian: Bhattacharyya & Gangopadhyay MPLA(00)ht/98.
In Other Theories > s.a. hamiltonian
systems; higher-order lagrangians; lagrangian
dynamics; M-theory; strings.
> In quantum mechanics:
What Isidro calls duality is in reality an ambiguity in the choice of complex
structure
used in quantizing a classical theory.
@ General references: Savit RMP(80);
Banerjee & Ghosh JPA(98)
[chiral oscillator model]; Olive ht/02-in.
@ Quantum mechanics:
Isidro
MPLA(03)qp,
PLA(03)qp, qp/03-in
[projective phase space], MPLA(04)qp/03 [torus
phase space]; > s.a. coherent states.
@ Non-abelian gauge theory: Mohammedi ht/95;
Duff IJMPA(96)
and IJMPD(96)
[in supersymmetric gauge theory, from strings]; Martín MPLA(99)
[in path space]; Chan & Tsou IJMPA(99)ht;
Tsou ht/00-ln,
ht/00-in;
Faddeev & Niemi PLB(02)ht/01 [SU(2)
Yang-Mills]; Majumdar & Sharatchandra
IJMPA(02);
Deser & Seminara PLB(05)ht [duality
invariance for free bosonic and
fermionic gauge
fields].
@ Sigma models: Mohammedi et al ZPC(97)ht/95;
Mohammedi PLB(96)ht/95,
PLB(96).
@ Linearized gravity: Henneaux
& Teitelboim PRD(05)gq;
Barnich & Troessaert JMP(09)-a0812 [as
bi-Hamiltonian system]; Bakas a0910.
@ General relativity: Hawking & Ross PRD(95)ht [electric
and magnetic black holes]; Maartens & Bassett CQG(98)gq/97;
Nouri-Zonoz et al CQG(99)gq/98 [NUT];
Dadhich
MPLA(99)gq/98,
MPLA(99),
GRG(00)gq/99;
Abramo et al MPLA(03)
[with scalar field]; Deser & Seminara PRD(05)ht [failure
in non-linear case]; Julia ht/05-in;
da Rocha & Rodrigues a0910 [in gravitational theories].
@ Scale factor duality in cosmology: Clancy et al CQG(98)gq;
Di Pietro gq/01/MPLA
[quintessence].
@ Related topics: Gaona & García IJMPA(07)
[first-order actions]; Lindström et al JHEP(08)-a0707 [T-duality
for generalized Kähler
geometries]; Barnich & Troessaert JHEP(09)-a0812 [for
spin-2 fields in Minkowski space].
> Related topics: see
gravitomagnetism; self-dual
fields [connections] and self-dual solutions in general
relativity [Weyl
tensor].
> Other dualities: see
Galerkin Duality.
Dual Mass in Gravitation
@ General references: Lubkin IJTP(77);
Magnon JMP(87), NCA(88);
Torre CQG(95)gq/94.
@ Phenomenology: Cates et al GRG(88);
Rahvar & Habibi ApJ(04)ap/03 [microlensing
signatures]; Danehkar a0707/MPLA.
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oct
2009